Symmetrization

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric. 1. Introduction Let (M n , g) be a smooth, closed Riemannian manifold of dimension n.

We deﬁne and study sl2 -categoriﬁcations on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reﬂection. We construct categoriﬁcations for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´’s abelian defect group conjecture for symmetric groups. e We give similar results for general linear groups over ﬁnite ﬁelds. ...

Steiner symmetrization is known not to increase perimeter of sets in Rn . The sets whose perimeter is preserved under this symmetrization are characterized in the present paper. 1. Introduction and main results Steiner symmetrization, one of the simplest and most powerful symmetrization processes ever introduced in analysis, is a classical and very well-known device, which has seen a number of remarkable applications to problems of geometric and functional nature.

Objectives of Chapter 3: To define the terms and the concepts of symmetric key ciphers; to emphasize the two categories of traditional ciphers: substitution and transposition ciphers; to describe the categories of cryptanalysis used to break the symmetric ciphers.

We present a novel approach for discovering word categories, sets of words sharing a signiﬁcant aspect of their meaning. We utilize meta-patterns of highfrequency words and content words in order to discover pattern candidates. Symmetric patterns are then identiﬁed using graph-based measures, and word categories are created based on graph clique sets. Our method is the ﬁrst pattern-based method that requires no corpus annotation or manually provided seed patterns or words.

USE OF MODERN BLOCK CIPHERS
Symmetric-key encipherment can be done
using modern block ciphers. Modes of
operation have been devised to encipher text of
any size employing either DES or AES.
Error Propagation
A single bit error in transmission can create errors in
several in the corresponding block.

USE OF MODERN BLOCK CIPHERS
Symmetric-key encipherment can be done using modern block ciphers. Modes of operation have been devised to encipher text of any size employing either DES or AES.
1 USE OF MODERN BLOCK CIPHERS
Electronic codebook (ECB) mode
Error Propagation A single bit error in transmission can create errors in several in the corresponding block. However, the error does not have any effect on the other blocks.

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S g+1 (X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the GromovWitten invariants of a point. 1. Introduction Let X be a smooth projective variety. The genus 0 Gromov-Witten invariants of X satisfy relations which imply that they can be completely encoded in the structure of a Frobenius manifold on the cohomology H ∗ (X, C). ...

This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar ﬁeld equations. For an open set of initial data whose closure contains in particular Reissner-Nordstr¨m data, o the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Penrose.
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